Friday, July 12, 2013

1307.3052 (Marco Benini et al.)

A C*-algebra for quantized principal U(1)-connections on globally
hyperbolic Lorentzian manifolds

Marco Benini, Claudio Dappiaggi, Thomas-Paul Hack, Alexander Schenkel
The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes of connections. The C*-algebra we construct generalizes the usual CCR-algebras since, contrary to the standard field-theoretic models, it is based on a presymplectic Abelian group instead of a symplectic vector space. We prove a no-go theorem according to which neither this functor, nor any of its quotients, satisfy the strict axioms of general local covariance. Yet, if we fix any principal U(1)-bundle, there exists a suitable category of sub-bundles for which a quotient of our functor yields a quantum field theory in the sense of Haag and Kastler. We shall provide a physical interpretation of this feature and we obtain some new insights concerning electric charges in locally covariant quantum field theory.
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